Recent work in the area of wireless communications has shown that when antenna placements in a two-by-two MIMO system are on the order of a symbol wavelength rather than the carrier wavelength, significant improvements can be made with respect to performance. This has given rise to the term of Signaling Wavelength Antenna Placement (SWAP) Gain to describe the advantages. The premise of this finding is that when the antennas are spaced a symbol wavelength apart, the likelihood that the channels are correlated is minimal.
However, determining the optimum placement of the antennas is seen as a highly non-linear problem that depends on the number of antennas in the system, and distribution of the users in the three-dimensional wireless communication space.
MIMO Systems
A MIMO system makes use of multiple antennas to exploit spatial diversity. By placing the antennas some distance apart, the received signals from the same user will appear at each antenna in the system. Since the radio channel in many systems is often impaired by effects such as random noise, multipath interference, co-channel interference (CCI), and adjacent channel interference, the resulting signals at each antenna will be different in terms of the channel impulse response [1], [2]. The noise and interference can be considered to be uncorrelated, while the message signal appearing at each antenna will retain some correlation. However, in cases where the antenna placements are similar, there exists the probability that the noise and interference will be correlated [3], [4], [5].
In general, any M-by-N MIMO system configuration can be modeled as a matrix of channel impulse functions from the Mth user to the Nth antenna. Typically, a wireless communications system will rely on a large base station that handles the requests from the mobile users in the cell. An example of a mobile user placement and antenna placement configuration of a four-by-four system is shown in FIG. 1.
In the research area of wireless communications, current generation systems are constantly being improved upon, with the advances becoming part of the next generation of standards. MIMO systems make use of multiple antennas to achieve spatial diversity and high performance [6], [7]. Recent work in the area of wireless communications has shown that when antenna placements in a two-by-two MIMO system are on the order of a symbol wavelength ([speed of light]/[symbol rate]), rather than the carrier wavelength, significant improvements can be made with respect to multiuser performance [8], [9], [10]. This has given rise to the term Signaling Wavelength Antenna Placement (SWAP) Gain to describe the advantages. The premise of this finding is that when the antennas are spaced a symbol wavelength, or more, the likelihood that the bits are correlated is minimal and the array receives more information. When used in conjunction with an ultra wideband (UWB) spectrum, the communication system holds the potential of delivering high-speed data services to many users [9], [11].
Much of the MIMO work to date relies heavily on assuming a randomized multipath rich environment to realize the maximum gains from spatial diversity [6], [12]. The fading characteristics are often modelled as Rayleigh distributions. However, in close range indoor situations, the Line of Signal (LOS) can often dominate the multipath components (modelled as Ricean distributions), minimizing the prospective gains from MIMO techniques. It is therefore necessary to examine MIMO performance in LOS situations.
Currently, the problem associated with effective MIMO UWB base station antennas is that they are large. The optimization of the MIMO UWB base station antenna is seen as a highly non-linear problem. Therefore, analytically a global optimization is difficult to achieve through traditional methods. An exhaustive trial-and-error method would be able to determine the optimal arrangement, but as the complexity of the system increases, the computational requirements for this method increase exponentially. Also, as wireless systems become ubiquitous, there exists the need to accommodate increasing data rates, but also increasing device numbers [13], [14].
By strategically arranging the antennas in the system to take advantage of the SWAP Gain, an optimal placement exists that will maximize the performance of the MIMO system in an LOS situation [15].
However, determining the optimum placement of antennas and arrangement of reflectors is seen as a highly non-linear computationally difficult problem that depends on the number of antennas in the system, placement and orientation of reflectors, the radio channel bandwidth, the symbol rate, fading, and the distribution of the users in the wireless communication cell [16], [1]. GA optimization has seen success in many non-linear applications, but often the results from these optimizations need interpretation [17], [18], [19]. The algorithm can converge to a local maxima/minima point rather than reach a global solution. The presence of these vestigial structures can prove to be a problem when attempting to gain information from the results. In such cases, it is important to evaluate the results in comparison to a known upper bound to give an indication on how well the GA optimization is performing.
Spread Spectrum Techniques
In code division multiple access (CDMA) systems, such as the Evolution-Data Optimized (EVDO) standard and direct sequence ultra wideband (DS-UWB), multiple users are multiplexed and transmitted over the same channel by using K-length pseudo random noise maximum length binary sequences, where K is the spreading factor [20], [21]. The resulting signal from a single user is thus increased in band-width by a factor of K. The summation of the signals from the total users produces an orthogonal signal set such that the original users signal can be de-multiplexed from the resultant signal by using the same generating code on the receive end of the channel [22], [23].
Some of the disadvantages of CDMA schemes are that they are affected more by multiple access interference (MAI) and intersymbol interference (ISI) [13]. To allow for this, a spreading factor greater than the expected capacity is used, resulting in a greater grade of service (GOS) at the expense of more bandwidth.
Symbol Wavelength
The symbol wavelength, λT, is defined as
                                          λ            T                    =                      c                          f              T                                      ,                            (                  Eq          .                                          ⁢          1                )            where c is the speed of light and fT is the symbol rate. It has been shown by Yanikomeroglu et al. [8], [10] that by placing antennas on the order of a chiplength that a greater diversity gain is achieved as opposed to traditional carrier wavelength spacing. For purposes of comparison, the antenna separations in the GA optimization simulation have been normalized with respect to the symbol wavelength.Radio Channel
The mobile radio channel is inherently noisy and cluttered with interference from other mobiles and multipath reflections. The overall performance of a wireless communication system is concerned with the multiple ways to improve the signal-to-interference-plus-noise Ratio (SINR). In 1948, Shannon demonstrated that through proper encoding in certain conditions, errors can be reduced to any desired level without sacrificing the rate of information transfer [24]. This led to what is known as Shannon's channel capacity formula given by
                              C          =                      B            ⁢                                                  ⁢                                          log                2                            ⁡                              (                                  1                  +                                      S                    N                                                  )                                                    ,                            (                  Eq          .                                          ⁢          2                )            where C is the channel capacity (bits per second), B is the transmission bandwidth (Hz), S is the signal power (W), and N is the noise power (W).LMS Adaptive Filter
The least mean square (LMS) adaptive filter is another proven concept that has shown great performance and widespread use due to its robustness and ease of implementation [16], [25], [26]. The basic setup of an LMS adaptive filter is shown in FIG. 2.
In this arrangement, the data stream to be transmitted is given by dn, a denotes the spreading code applied to the data, b represents the wireless channel response, ηn is the Additive White Gaussian Noise (AWGN), rn is the signal received at the antenna, Wn is the adaptive filter coefficient, d′n is the filtered received signal, en is the error associated with the filtered received signal, and n is the discrete-time index.
During training, the receiver knows dn, as the training sequence would be programmed into the adaptive filter logic. It will then update the filter coefficient Wn according toWn+1=Wn+μenrn  (Eq. 3)where Wn+1 is the updated filter coefficient, Wn is the current filter coefficient, and μ is the LMS adaptation constant, which is chosen to be small enough such that the filter will converge. If μ is chosen to be too large, the adaptation will diverge and the minimum mean square error (MMSE) will not be reached.
After the filter has finished processing the training sequence, the filter then switches from operating on the training sequence and continues to adapt from the incoming signal. Ideally at this point the adaptive filter has converged and has successfully performed the channel inversion to create a matched filter and remains at the global minimum rather than diverging off to some other local minimum. Generalizing this scalar example to vectors leads to the usual formWn+1=Wn+μenrn  (Eq. 4)
where Wn+1 is vector of the updated filter coefficients, Wn, is a vector of the current filter coefficients, μ is the LMS adaptation constant, en is a vector of the error associated with the filtered receive signal, and rn is a vector of the signals received at the antenna.
Genetic Algorithms
GA optimization borrows on the ideas of evolution found in the everyday biology of living organisms. First discussed in Charles Darwin's Origin of Species, the concept is that every living organism that exists today is a result of a process of evolution over the many generations that the population has existed for over great lengths of time. Within every cell of an organism, a genetic blueprint is contained within a chemical substance called deoxyribonucleic acid (DNA). This chemical substance is in a double-helical structure and contains continuous base pairs of the nucleotides adenine (A), thymine (T), guanine (G) and cytosine (C). The sequencing of these nucleotides provides the basic genetic code that is capable of completely reproducing the organism in which the DNA is contained [17], [18]. Thus, the term DNA becomes synonymous with the minimum number of describing features that is required to fully recreate an individual or organism.
Translating this to science and engineering problems, a set of possible solutions becomes the population of living organisms. This population is then evaluated to determine their fitness to performing the desired goal defined in the problem. Such as in nature, the individuals are then subjected to a survival of the fittest evaluation, where only a portion of the top performing individuals are retained for the next generation. These top performing individuals are also chosen to be the parents for the succeeding population. These parents then generate offspring to fill the population. The offspring are generated in primarily two mechanisms, through crossover and mutation.
One of the advantages of GAs is that they are capable of operating on a problem that has a very large set of possible solutions [17], [19]. A problem with a large set of solutions may not be computationally practical to investigate through “brute force” methods. This leads to the advantage that genetic algorithms will often lead to solutions that would otherwise not have been reached through common numerical techniques.